In this paper we focus on dynamic thermal management(DTM) strategies that use dynamic voltage scaling (DVS)for power control. We perform a theoretical analysis targeted atestimating the optimal strategy, and show two facts: (1) whenthere is a gap between the initial and the limit temperatures,it is best to start with a high (though not necessarily maximal)frequency and decrease it exponentially until the limit temperatureis reached; (2) when being close to the limit temperature,the best strategy is to stay there. We use the patterns exhibitedby the optimal strategy in order to analyze some existing DTMtechniques.